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Morse homology

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Published by Birkhäuser Verlag in Basel, Boston .
Written in English

Subjects:

  • Morse theory.,
  • Homology theory.

Book details:

Edition Notes

Includes bibliographical references (p. [229]-231) and index.

StatementMatthias Schwarz.
SeriesProgress in mathematics ;, v. 111, Progress in mathematics (Boston, Mass.) ;, v. 111.
Classifications
LC ClassificationsQA331 .S43 1993
The Physical Object
Paginationix, 235 p. :
Number of Pages235
ID Numbers
Open LibraryOL1411871M
ISBN 100817629041
LC Control Number93020738

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: Morse Homology (Progress in Mathematics) (): Schwarz: Books. Skip to main content Hello, Sign in. Account & Lists Sign in Account & Lists Returns & Orders. Try Prime Cart. Books. Go Search Hello Select your address. Background The subject of this book is Morse homology as a combination of relative Morse theory and Conley's continuation principle. Classical Morse Theory The fact that Morse . Introduction Background The subject of this book is Morse homology as a combination of relative Morse theory and Conley's continuation principle. The latter will be useda s an instrument to express the homology encoded in a Morse complex associated to a fixed Morse function independent of this function. Morse Theory and Floer Homology Michèle Audin, Mihai Damian (auth.) This book is an introduction to modern methods of symplectic topology.

This book is based on the lecture notes from a course we taught at Penn State University during the fall of The main goal of the course was to give a complete and detailed proof of the Morse Homology Theorem (Theo­ rem ) at a level appropriate for second year graduate students. The resulting Morse homology will de ne an invariant of the smooth manifold that is equivalent to its singular homology. We will use this equivalence to prove Poincar e duality and the Morse inequalities. We will also compute some examples Morse homology groups. The primary reference used is Hutchings’s lecture notes on Morse homology [2]. 2. In these notes we focus on the instanton Floer homology of a homology three-sphere, which is the Morse homology of the Chern-Simons functional. Defined on the infinite dimensional space of gauge equivalence classes of -connections on and being circle-valued, this functional brings in further features not present in classical Morse homology. A book that is tough to read, but is a gateway to Floer theory is Schwarz' book. Schwarz, Matthias Morse homology. Progress in Mathematics, Birkhäuser Verlag, Basel, I heard good things about the book of Audin and Damian, but I have not read it. Audin, Michèle; Damian, Mihai Morse theory and Floer homology.

Morse homology also serves a simple model for Floer homology, which is covered in the second part. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. Morse homology can also be formulated for Morse–Bott functions; the differential in Morse–Bott homology is computed by a spectral sequence. Frederic Bourgeois sketched an approach in the course of his work on a Morse–Bott version of symplectic field theory, but this work was never published due to substantial analytic difficulties. This approach to Morse–Bott homology appeared in the context of unpublished work for contact homology by Bourgeois, in which the critical submanifolds are the sets of Reeb orbits, and the gradient flows between the critical submanifolds are pseudoholomorphic curves in the symplectization of a contact manifold asymptotic to Reeb orbits in the relevant critical manifolds of Reeb orbits. If we extend each Morse . Morse Homology | Background The subject of this book is Morse homology as a combination of relative Morse theory and Conley's continuation principle. The latter will be useda s an instrument to express the homology encoded in a Morse complex associated .